📐 Parabola Calculator

Calculate parabola properties

Distance from vertex to focus (p ≠ 0)

How to Use This Calculator

1

Enter Vertex Coordinates

Input the x and y coordinates (h, k) of the parabola's vertex.

2

Enter Parameter p

Input the parameter p (distance from vertex to focus). p cannot be zero.

3

Calculate

Press "Calculate Parabola" to find vertex, focus, directrix, and equation.

Formula

Standard form: (x - h)² = 4p(y - k)

Vertex: (h, k), Focus: (h, k + p), Directrix: y = k - p

About Parabola Calculator

The Parabola Calculator finds the vertex, focus, directrix, and equation of a parabola given its vertex coordinates and parameter p.

When to Use This Calculator

  • Conic Sections: Analyze parabola properties
  • Geometry: Calculate parabola characteristics
  • Physics: Model projectile motion and reflections

Frequently Asked Questions

What is a parabola?

A parabola is a U-shaped curve defined as all points equidistant from a focus point and a directrix line. Standard form: (x - h)² = 4p(y - k) for vertical parabolas.

What is parameter p?

Parameter p is the distance from the vertex to the focus. It determines how "wide" or "narrow" the parabola is. Larger |p| means wider parabola.